Elliptical Orbits



[1]Elliptical Orbits

Name________________________________

Date _________________________

Aim.

You will be able to:

• Explain how to draw an ellipse

• Relate the shape of an ellipse to the shape of the objects’ orbits around the sun

Materials Needed

For each student

• A copy of the worksheet, printed or virtual

• A 25cm. x 30cm piece of cardboard as a backing

• Three blank sheets of A4 paper

• Pencil

• A 20 an long piece of string

• Two push pins, one yellow and one white

• A ruler

• Sticky tape

Steps

1. Tie the ends of the string together so that they make a loop.

2. Fold the paper in half vertically and draw a vertical line on the fold to

locate the mid-line of the paper.

3. Determine the midpoint of the vertical fold line. Mark the point with a pencil.

This point will be the centre of the ellipse.

4. Tape the corners of the piece of paper to the cardboard.

5. Put the first push pin into the cardboard at the midpoint.

6. Place the yellow push pin in the cardboard 1 cm from the yellow push pin.

7. Loop the string around the push pins.

8. Using your pencil, draw around the string, as shown in the diagram.

9. Remove the white push pin and string from your diagram and label it “Orbit #1.”

10. Repeat steps 6-9 for the rest of the orbits. The second time, place the white push

pin 6 cm from the yellow push pin in a different direction than the first.

Questions

For all

1. The orbits of the planets and comets around the Sun all are shaped like ellipses. Ellipses have two __________________________________________

2. According to Kepler’s First Law, what object in the Solar System should one of

the foci represent? ____________ .

Extension

Measure the length of the major axes of each of the three orbits, in centimetres. Record your answers in the table below. To ensure that you measure the full length of the major axis, line up your ruler along the ellipse’s foci.

Eccentricity= Distance between foci divided by the Length of major axis

1. Use this equation to calculate the eccentricities of the three orbits. Record

your answers in the table below.

|Orbit |Distance Between Foci (cm) |Length of Major |Eccentricity |

| | |Axis (cm) | |

|Orbit 1 |1 cm | | |

|Orbit 2 |6 cm | | |

|Orbit 3 |7 cm | | |

2. A circle is a form of ellipse with its eccentricity equal to .

Hint If there is only one focus point (the centre), The distance between them is zero. Zero divided by any number is ?

Why . . .

In our Solar System, objects orbit the Sun in paths that are shaped like ellipses,

with the Sun at one of the focal points. Some of the orbits in the Solar System

are shaped more nearly like a circle and others have a more eccentric orbit. In other words, the focal points of their ellipses are farther apart.

Some comets have very eccentric orbits, travelling near the Sun during part of their orbits, and beyond the outer planets at other points in their orbits. Knowing about orbits helps us to predict the positions of planets and chart courses for spacecraft.

Optional Lets draw some orbits using Paint

• Open Paint, click on Images ( Attributes and set the picture to be 640 x 480 pixels.

• Click on the Ellipse tool, and then hold down the Shift key while to draw a circle in the middle of the page. This will be your sun. Colour it orange if you wish.

• Now draw some ellipses around the “sun”. You can change your line colour and thickness if you wish.

• Experiment with the “flatness” or eccentricity of the ellipses.

• Next, move your curser to the top or bottom of the page away from your previous drawing.

• Draw a long flat ellipse that you will be able to fit a selection box around.

• Select this ellipse, and click on Image ( Stretch/Skew.

• Skew it 40 degrees to the vertical and drag the skewed ellipse over the others.

Be Sure to have the paste tool as,” show background”

• This skewed ellipse can mimic either the orbit of Pluto, or if you draw a really flat ellipse, the orbit of comets.

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[1] From an article Originally published in The Technology Teacher, April 1999, by the International Technology Education Association, and published on the net by NASA at

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